Backflow Dynamics of Newtonian Fluids in an Elastic Fracture with Slip Walls

Zeighami, Farhad; Lenci, Alessandro; Longo, Sandro; Federico, Vittorio Di

doi:10.3390/environsciproc2022021045

Cited by 1 publication

(7 citation statements)

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“…It is worth noting that in the absence of external pressure, the ODE of Equation ( 17) admits a semi-analytical solution, as documented in Ref. [28]. These semi-analytical results are superimposed on Figure 3d using red dots, revealing a good agreement with our numerical predictions.…”

Section: Time Evolution Of Fracture Aperturesupporting

confidence: 83%

“…where N s is a slip number expressing the slip length in the dimensionless form [28] and the time and pressure scales t c and p c are The initial and boundary conditions expressed in the dimensionless form are:…”

Section: Problem Formulationmentioning

confidence: 99%

“…which needs to be integrated over time with the initial condition given by the first expression in Equation ( 14). Noteworthy, Equation ( 17) reduces to the following cases: (i) no-slip Newtonian flow [26] for n = 1, N s = 0; (ii) no-slip power-law flow [27] for N s = 0; (iii) slip Newtonian flow [28] for n = 1 and N s = 0. The first two are amenable to an analytical solution, while the third requires a numerical approach, as does the present case.…”

Section: Solutionmentioning

confidence: 99%

“…Red dots superimposed to (d) highlight the analytical solution for the specific case of n = 1 and P e = 0 adopted from Ref. [28].…”

Section: Time Evolution Of Fracture Aperturementioning

confidence: 99%

“…This scheme was first adopted in the pioneering paper of Dana et al [26], who studied the backflow of a Newtonian fluid; later works of theoretical and experimental nature expanded on the topic of relaxation-induced flow in fractures by adopting a power-law [27] non-Newtonian constitutive equation. More recently, slipping walls [28] were added to the schematic in conjunction with Newtonian flow; the main finding was that slip at the fracture walls is a delaying factor towards the fracture closure. In the present work, we combine the power-law rheology with slip flow, which, in turn, is often associated with non-Newtonian flow behavior [29].…”

Section: Introductionmentioning

confidence: 99%

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This research delves into the complexities of backflow phenomena in finite-length and flat-walled fractures with elastic walls, specifically focusing on power-law fluids, whose shear-thinning behavior distinguishes them from Newtonian fluids. We model the backflow process under the lubrication approximation and by incorporating the linear Navier slip law. We numerically examine the influence of parameters such as slip length, fluid rheology, and external pressure on the backflow propagation of the carrier fluid. Our findings underscore the significant role played by the rheological index in determining the fracture closure rate. Additionally, our investigations highlight the marked effect of external pressure variations on pressure distribution within the fracture. Notably, the friction coefficient at the fracture walls, as denoted by a dimensionless slip number, exhibits limited influence on the fundamental dynamics of the problem. These insights advance our understanding of power-law fluid backflow and have wide-ranging applications across various engineering disciplines.

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Section: Time Evolution Of Fracture Aperturesupporting

confidence: 83%

Section: Problem Formulationmentioning

confidence: 99%